Gubbins D., Herrero-Bervera E. Encyclopedia of Geomagnetism and Paleomagnetism

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the terrestrial climate. The magnetic field also plays a major role in the

evolution of the Sun as a star, with magnetic braking drastically reducing

the angular momentum of the star as it evolves over its lifetime (Mestel,

1999).

This article will review the observations of the solar magnetic field

and briefly indicate the features that need to be understood in order to

formulate a theory for the generation and evolution of such a field.

The large-sca le solar field

Although magnetic fields in the Sun are observed on a whole spectrum

of length-scales, it is usual to classify magnetic phenomena either as

large- or small-scale events. Here the large-scale magnetic field is

defined to be that which is observed on scales comparable to the solar

radius, with systematic properties, spatial organization, and temporal

coherence.

The most obvious manifestation of the large-scale solar magnetic

field is the appearance of sunspots at the solar surface. Sunspots have

been systematically observed in the West since the early 17th century

when Galileo utilized the newly invented telescope to document the

passage of dark spots across the solar surface. Although the 11-year

period for the cycle of sunspot activity was discovered by Schwabe

in 1843, the connection between sunspots and the magnetic field of

the Sun was only determined when Hale in 1908 used the Zeeman

splitting of spectral lines to establish the presence of a strong magnetic

field in sunspots (Hale, 1908). By then it could clearly be seen that

sunspots appear in bipolar pairs, with a leading and trailing spot nearly

aligned with the solar equator. Magnetic observations of sunspots indi-

cate that they have systematic properties—often described as Hale’s

polarity laws. These state that the magnetic polarities of the leading

and trailing spots are opposite, with the sense of the polarity being

opposite in each hemisphere of the Sun (see Figure M27). Moreover,

the polarities of the bipolar sunspot pairs that are observed at the solar

surface reverse after each minimum in sunspot activity. Finally, Joy’s

law states that there is a systematic tilt (of the order of 4



) in the align-

ment of sunspot pairs with respect to the solar equator, with the lead-

ing spot being closer to the equator. Taken together, these indicate that

sunspots are the surface manifestation of an underlying magnetic field

with an opposite sense in each hemisphere. This magnetic field is

cyclic, with a mean period of 22 years.

Sunspot pairs are interpreted as an indicator for an azimuthal (toroi-

dal) B

field. A radial (poloidal) component of the magnetic field, B

may also be detected. The radial field is particularly visible at the solar

poles with a distinct and opposite polarity at each pole. This polar field

reverses at the maximum of sunspot activity and the polarity is such

that between solar maximum and solar minimum the radial field has

the same polarity as the trailing spots of the sunspot pairs in the same

hemisphere. Hence B

and B

fields are nearly in antiphase with

< 0 for most of the time (Stix, 1976). Also particularly visible

at high latitudes are ephemeral active regions. These are small regions

that do not systematically obey Hale’s polarity laws (although they do

show a preference for the same orientation as sunspots) and have a

lifetime of a few days. It is now believed that these ephemeral active

regions are either reprocessed flux from active regions or the result

of local regeneration in the solar convection zone.

An important measure of the topology of the large-scale solar mag-

netic field is given by the current helicity of the magnetic field

¼hj  Bi, where j ¼ 1=m

rB is the electric current. This is a

difficult quantity to measure, although some information about the

radial contribution to the current helicity h j

i can be estimated from

vector magnetograms of active regions. The measurements are consis-

tent with the premise that magnetic structures possess a preferred

orientation corresponding to a left-hand screw in the northern hemi-

sphere (with an opposite sense in the southern hemisphere). Another

crucial topological measure of the magnetic field is the magnetic heli-

city H¼hA  Bi (where B ¼rA). Although some estimates have

been made of the magnetic helicity from vector magnetograms, it is

almost impossible to measure this important property of the solar mag-

netic field with any great certainty.

Spatiotemporal variability

In addition to the systematic properties of the solar magnetic field indi-

cated by Hale’s and Joy’s laws, these large-scale features follow a sys-

tematic spatiotemporal pattern. At the beginning, of a cycle spots

appear on the Sun at latitudes of around 27



; as the cycle progresses

the location of activity drifts toward the equator and the spots then die

out (at a latitude of around 8



) in the next minimum. It is important

to note that it is the location of magnetic activity rather than individual

sunspot pairs—which have a lifetime of at most a few months—that

migrates toward the solar equator. This migration of activity produces

the familiar butterfly diagram first exhibited by Maunder (1913). An

up-to-date version showing the incidence of sunspots as a function

Figure M26/Plate 14a Compound extreme ultraviolet (171 A

)

full-disk image of the Sun taken by the Transition Region and

Coronal Explorer (TRACE) satellite. The two bands on either side

of the Sun’s equator contain bright features indicating magnetic

activity.

Figure M27 Hale’s polarity law: Magnetogram of the solar surface

as a function of longitude and latitude. White indicates strong

radial field pointing out of the solar surface, while black indicates

strong radial field pointing into the solar surface. Notice that the

sense of the active regions is opposite in the northern and

southern hemispheres.

506 MAGNETIC FIELD OF SUN

of colatitude is in Figure M28a. It is clear from this figure that the

level of sunspot activity has been approximately the same in each

hemisphere, and that the solar magnetic field has a high degree of

symmetry. The above observations indicate that the solar field is pri-

marily axisymmetric and dipolar, although a small nonaxisymmetric

component of the solar field has been observed.

In addition to the basic solar cycle, sunspot activity undergoes

further significant temporal variability. By using the (arbitrarily

defined) sunspot number (e.g., Eddy, 1976), the variation in magnetic

activity over the past 400 years may be obtained. An up-to-date record

of sunspot numbers is shown in Figure 28b. This figure shows that an

average cycle is temporally asymmetric, with a sharp rise from mini-

mum to maximum of duration 3–6 years being followed by a gradual

decay lasting between 5 and 8 years. The amplitude of the cycle has

been shown to be anticorrelated with the length of the rise time and

that of the solar cycle itself. The solar cycle appears to be chaotic with

an amplitude that is modulated aperiodically. Despite the shortness of

the time sequence, the existence of a characteristic timescale for the

modulation of approximately 90 years (the Gleissberg cycle) has been

postulated—although this is open to debate. What is clear, however, is

the presence in the record of an episode with a dearth of sunspots,

which lasted for about 70 years at the end of the 17th century. This

interruption is known as the Maunder minimum. There is no doubt that

this is a real phenomenon, and this is not due to the lack of awareness

on the part of the observers (see Ribes and Nesme-Ribes, 1993). It is

also interesting to note that at the end of the Maunder minimum

large-scale solar magnetic activity started again primarily in the south-

ern hemisphere of the Sun and hence the field was not dipolar for a

cycle. Although small asymmetries between sunspot activity in the

northern and southern hemispheres have been observed since the

Maunder minimum, when the field is strong the field is largely dipolar,

with only a small quadrupole component as noted above. It is only

when the field is weak and the dipole component is small that a com-

parable quadrupolar contribution can be seen.

More useful information about the temporal variability of the solar

magnetic activity can be gained by the use of proxy data (see e.g.,

Beer, 2000). Magnetic fields in the solar wind modulate the cosmic

ray flux entering the Earth’s atmosphere. These high-energy particles

lead to the production of radioisotopes, including

Be and

and so the abundance of these isotopes can act as a measure of solar

magnetic activity—the abundance is anticorrelated with magnetic

activity. The isotope

Be is preserved in polar ice-cores and its produc-

tion rate, together with the sunspot number, is shown in Figure M29.

The figure clearly shows the presence of the Maunder minimum and

that, although sunspot activity is largely shut off during this period,

cyclic magnetic activity continued with a period of approximately 9

years. The

Be record extends back over 50 ka and analysis of this

record clearly shows both continued presence of the 11-year solar

cycle. Moreover analysis indicates that the Maunder minimum is not

an isolated event, with regularly spaced minima (termed grand minima)

interrupting the record of activity with a significant recurrent timescale

of 205 years (Wagner et al., 2001). The variations in

C production

confirm this pattern of recurrent grand minima with a timescale of

about 200 years. Moreover, both of these radioisotope records show

significant power at a frequency that corresponds to roughly 2100

years. It appears as though grand minima occur in bursts, with this as

a well-defined period of recurrence (J. Beer, private communication).

Taken together, these data indicate that the solar magnetic field

undergoes a considerable amount of temporal variability on scales

varying from days to hundreds of years.

The small-scale solar magnetic field

In addition to the large-scale magnetic field with systematic properties

described above, magnetic field is also observed on scales comparable

with the solar convective scales and smaller. The magnetic network is

seen to coincide largely with the network forming the boundaries of

supergranular convection. The network has a different form at solar

maximum and minimum. At solar minimum it consists of mixed polar-

ity, vertically oriented bundles of magnetic flux, while at solar maxi-

mum the network is dominated by the presence of large unipolar

regions in close proximity to the bipolar active regions. The magnetic

network is therefore only weakly linked to the solar magnetic cycle.

The flux bundles in the magnetic network are dynamic and are

observed to move randomly across the solar surface, with a motion

that is consistent with two-dimensional diffusion.

The magnetic network is also interspersed with weak stochastic

magnetic fields of random orientations. This intranetwork field is

Figure M28 (a) Solar butterfly diagram: Location of sunspots as a function of time (horizontal axis) and latitude (vertical axis). As the

cycle progresses sunspots migrate from midlatitudes to the equator. (Courtesy of D.N. Hathaway). (b) Time series for yearly sunspot

group numbers. Notice the Maunder minimum at the end of the 17th century.

MAGNETIC FIELD OF SUN 507

weaker than the network field and has a significantly shorter dynami-

cal timescale associated with it (on the scale of days as opposed to

months). There appears to be little or no correlation of this field with

the solar cycle and the behavior of this field is consistent with it being

generated by the action of a local dynamo (see Dynamo, solar) situ-

ated in the upper reaches of the solar convection zone. All these

small-scale magnetic features visible at the solar surface migrate

slowly toward the solar pole with a velocity of between 1 and 10 m s

–1

This migration is due to the presence of a systematic large-scale meri-

dional flow at the solar surface. The meridional flow has also been

detected by helioseismic inversions of the solar interior and is belie-

ved to continue poleward to a depth of 0:9R



, where R



is the solar

radius.

Solar cycle indices—irradiance, flows and the shape

of the corona

The solar magnetic cycle can not only be detected in the large-scale

magnetic features such as sunspots. Many other solar indices follow

the 11-year activity cycle. Of particular interest terrestrially is the var-

iation in the solar luminosity (the so-called solar constant) that occurs

over the solar cycle. Total solar irradiance does vary systematically in

phase with the solar cycle. In the visible spectrum the modulation var-

ies only weakly, with the effect of bright magnetic faculae nearly

exactly canceling out (but just overcoming) that of dark sunspots.

However in the far-ultraviolet and X-ray part of the spectrum the mod-

ulation is large and systematic (see e.g., Frölich, 2000). The shape of

the solar corona and strength of the solar wind is also correlated with

the solar cycle, and these in turn interact with the geomagnetic field

and are measurable in the AA and AP geomagnetic indices and visible

in the record of aurorae.

In addition, the presence of the magnetic field is also responsible for

driving flows that are correlated with the solar activity cycle. This pat-

tern of parallel belts of faster slower rotation was initially discovered

by Doppler measurements of the solar surface and dubbed torsional

oscillations. It is now known from helioseismic inversions for the

internal solar rotation (Vorontsov et al., 2002) that these oscillations

have an amplitude of approximately 5–10 m s

–1

and that they extend

deep into the solar interior—reaching at least halfway into the solar

convective zone (see Figure M30/Plate 14b). These bands of zonal

flows, which have an equatorward and poleward propagating branch,

have a period of 11 years, which is consistent with them being driven

by the Lorentz force associated with the magnetic field.

Stellar magnetic fields

The Sun is just one example of a moderately rotating star whose mag-

netic properties can be observed in detail. Much can be learned about

the magnetic behavior of the Sun, by examining the properties of

nearby magnetically active stars that have similar properties (e.g., age

and rotation rate). The most important results indicating magnetic

activity in stars are obtained by measuring the level of Ca

, H, and

K emission. The rate of Ca

emission in the Sun is well-known

to be correlated with solar magnetic fields. Results from the Mount

Wilson Survey indicate the level of magnetic activity in a relatively

large sample of slow and moderate rotators. It is now clear that, for

stars of a fixed spectral type, there is a range of activity, but that this

scatter is a function of age. It can be shown that the level of activity

in a star can be represented as a function of the inverse Rossby (or

Coriolis) number s ¼ Ot

, where O is the angular velocity of the star

and t

is a suitable convective timescale (Brandenburg et al., 1998).

For slow rotators, cyclic magnetic activity may be deduced from var-

iations in the Ca

emission and it is clear that the cycle period of activity

decreases with increasing rotation rate. Moreover as the rotation rate is

increased the magnetic activity of the stars becomes more disordered,

with a transition between cyclic, doubly periodic and chaotic activity

occurring as the rotation rate is increased. On studying this relationship

in greater detail it becomes apparent that the stars fall into two distinct

groups, an active and an inactive branch (Brandenburg et al., 1998). This

is enough to discourage the extension of the properties of slowly rotating

stars to cover those with a greater angular momentum.

Direct measurement of magnetic fields in stars is also possible using

a variety of techniques, including broadband polarimetry and photo-

metry (see e.g., Rosner, 2000). The luminosity of a highly active star

may vary by up to 30%, whereas the known variation in solar lumin-

osity is only 0.2%. Whether an increase in magnetic activity in a star is

positively or negatively correlated with an increase in luminosity

depends upon the absolute level of activity in the star. It is also found

Figure M29 Comparison of the proxy

Be data from the dye 3 ice

core (measured in 10000 atoms g

–1

), filtered using a low pass

(6 year) filter, with the filtered (6 year) sunspot group number as

determined by Hoyt and Schatten (1998). Note that the

Be is

anticorrelated with sunspot activity.

Figure M30/Plate 14b Top panel: The rotational variation as a

function of time and latitude at radius r ¼ 0:98R



are shown for the

first nearly 6 years, and thereafter the time series is continued by

exhibiting the 11-year harmonic fit. Shown to the right are the

residuals from the fit, on the same color scale. Bottom panel: As for

above, but showing the rotation variation as a function of depth

instead of latitude, at latitude 20



. (From Vorontsov et al., 2002).

508 MAGNETIC FIELD OF SUN

that the level of magnetic activity is proportional to the inverse Rossby

number of the star—a result that is consistent with the emission

data. Clearly, as there is a small sample of stars for which we have a

detailed record of magnetic activity and this record is comparatively

short, there is a need to continue these observations as they give

us great understanding of the magnetic properties of our nearest

star—the Sun.

S. Tobias

Bibliography

Beer, J., 2000. Long-term indirect indices of solar variability. Space

Science Reviews, 94:53–66.

Brandenburg, A., Saar, S.H., and Turpin, C.R., 1998. Time evolution

of the magnetic activity cycle period. The Astrophysical Journal,

498: L51–L54.

Eddy, J.A., 1976. The Maunder minimum. Science, 192: 1189–1202.

Fröhlich, C., 2000. Observations of irradiance variations. Space

Science Reviews, 94:15–24.

Hale, G.E., 1908. On the probable existence of a magnetic field in sun-

spots. Astrophysics Journal, 28: 315–343.

Hoyt, D.V., and Schatten, K.H., 1998. The Role of the Sun in Climate

Change. New York: Oxford University Press.

Maunder, E.W., 1913. Note on the distribution of sunspots in helio-

graphic latitude. Monthly Notices of the Royal Astronomical

Society, 64: 747–761.

Mestel, L., 1999. Stellar Magnetism. Oxford: Clarendon Press.

Ribes, J.C., and Nesme-Ribes, E., 1993. The solar sunspot cycle in the

Maunder minimum AD 1645–AD 1715. Astronomy and Astrophy-

sics, 276: 549–563.

Rosner, R., 2000. Magnetic fields of stars: using stars as tools for

understanding the origins of cosmic magnetic fields. Philosophical

Transactions of the Royal Society of London, Series. A, 358:

689–708.

Stix, M., 1976. Differential rotation and the solar dynamo. Astronomy

and Astrophysics, 47: 243–254.

Wagner, G. et al., 2001. Presence of the solar de vres cycle (205

years) during the last ice age. Geophysical Research Letters,

28: 303.

Vorontsov, S.V., Christensen-Dalsgaard, J., Schou, J., Strakhov, V.N.,

and Thompson, M.J., 2002. Helioseismic measurement of solar

torsional oscillations. Science, 296: 101–103.

Cross-references

Dynamo, Solar

MAGNETIC INDICES

Magnetic indices are simple measures of magnetic activity that occurs,

typically, over periods of time of less than a few hours and which is

recorded by magnetometers at ground-based observatories (Mayaud,

1980; Rangarajan, 1989; McPherron, 1995). The variations that

indices measure have their origin in the Earth’s ionosphere and magne-

tosphere. Some indices having been designed specifically to quantify

idealized physical processes, while others function as more generic

measures of magnetic activity. Indices are routinely used across the

many subdisciplines in geomagnetism, including direct studies of the

physics of the upper atmosphere and space, for induction studies of

the Earth’s crust and mantle, and for removal of disturbed-time mag-

netic data in studies of the Earth’s deep interior and core. Here we

summarize the most commonly used magnetic indices, using data from

a worldwide distribution of observatories, those shown in Figure M31

and whose sponsoring agencies are given in Table M1.

Range indices K and K

The 3-h K integer index was introduced by Bartels (1938) as a mea-

sure of the range of irregular and rapid, storm-time magnetic activity.

It is designed to be insensitive to the longer term components of mag-

netic variation, including those associated with the overall evolution of

a magnetic storm, the normal quiet-time diurnal variation, and the very

much longer term geomagnetic secular variation arising from core con-

vection. The K index is calculated separately for each observatory,

and, therefore, with an ensemble of K indices from different observa-

tory sites, the geography of rapid, ground level magnetic activity can

be quantified.

When it was first implemented, the calculation of K relied on the

direct measurement of an analog trace on a photographic record.

Today, in order to preserve continuity with historical records, computer

programs using digital data mimic the original procedure. First, the

diurnal and secular variations are removed by fitting a smooth curve

to 1-min horizontal component (H) observatory data. The range of

the remaining data occurring over a 3-h period is measured. This is

then converted to a quasilogarithmic K integer, 0, 1, 2, ..., 9, accord-

ing to a scale that is specific to each observatory and which is designed

to normalize the occurrence frequency of individual K values among

the many observatories and over many years.

A qualitative understanding of the K index and its calculation can be

obtained from Figure M32. There we show a trace, Figure M32a,of

the horizontal intensity at the Fredericksburg observatory recording

magnetically quiet conditions during days 299–301 of 2003, followed

by the sudden commencement in day 302 and the subsequent develop-

ment of the main and recovery phases of the so-called great Halloween

Storm. In Figure M32b we show, on a logarithmic scale, the range of

the Fredericksburg data over discrete 3-h intervals, and in Figure M32c

we show the K index values themselves. Note the close correspon-

dence between the magnetogram, the log of the range and the K index.

This storm is one of the 10 largest in the past 70 years since continu-

ous measurements of storm size have been routinely undertaken. For

more information on this particular storm, see the special issue of the

Journal of Geophysical Research, A9, 110, 2005.

Planetary-scale magnetic activity is measured by the K

index

(Menvielle and Berthelier, 1991). This is derived from the average of

fractional K indices at 13 subauroral observatories (Table M1) in such

a way as to compensate for diurnal and seasonal differences between

the individual observatory K values. The final K

index has values

0, 0:3, 0 :7, 1:0, 1:3, ... etc. For illustration, in Figure M33 we show

magnetograms from the 13 observatories contributing to K

, recording

the Halloween Storm of 2003, along with the K

index itself. The dis-

tribution of observatories is far from uniform, with a predominant

representation from North America and Europe, and very little repre-

sentation from the southern hemisphere. In fact, in Figure M33,itis

easy to see differences during the storm in the magnetograms among

the different regional groupings of observatories. Although geographic

bias is an obvious concern for any index intended as a measure of pla-

netary-scale magnetic activity, K

has proven to be very useful for

scientific study (e.g., Thomsen, 2004). And, since it has been continu-

ously calculated since 1932, K

lends itself to studies of magnetic dis-

turbances occurring over many solar cycles.

There are several other indices related to the K and K

. A

and A

are linear versions of K and K

. K

, A

, K

, and A

are similar to K

and A

except that they use, respectively, northern and southern hemi-

sphere observatories; their global averages are K

and A

. The aa

index is like the K

except that it utilizes only two, roughly antipodal,

observatories, one in the northern hemisphere and one in the southern

hemisphere. aa has been continuously calculated since 1868, making it

one of the longest historical time series in geophysics.

Auroral e lectrojet indices AU, AL, AE, AO

During magnetic storms, particularly during substorms, magneto-

spheric electric currents are often diverted along field lines, with

MAGNETIC INDICES 509

current closure through the ionosphere. To measure the auroral zone

component of this circuit, Davis and Sugiura (1966) defined the aur-

oral electrojet index AE. Ideally, the index would be derived from data

collected from an equally spaced set of observatories forming a neck-

lace situated underneath the northern and southern auroral ovals.

Unfortunately, the southern hemispheric distribution of observatories

is far too sparse for reasonable utility in calculating AE, and the north-

ern hemispheric observatories only form a partial necklace, due to the

present shortage of reliable observatory operations in northern Russia.

Progress is continuing, of course, to remedy this shortcoming, but for

Table M1 Summary of index observatories used here

Agency Country Observatory Observatory Index

Geoscience Australia Australia Canberra CNB K

Geological Survey of Canada Canada Fort Churchill FCC AE

Geological Survey of Canada Canada Meanook MEA K

Geological Survey of Canada Canada Ottawa OTT K

Geological Survey of Canada Canada Poste-de-la-Baleine PBQ AE

Geological Survey of Canada Canada Yellowknife YKC AE

Danish Meteorological Institute Denmark Brorfelde BFE K

Danish Meteorological Institute Denmark Narsarsuaq NAQ AE

GeoForschungsZentrum Potsdam Germany Niemegk NGK K

GeoForschungsZentrum Potsdam Germany Wingst WNG K

University of Iceland Iceland Leirvogur LRV AE

Japan Meteorological Agency Japan Kakioka KAK D

Geological and Nuclear Science New Zealand Eyerewell EYR K

National Research Foundation South Africa Hermanus HER D

Swedish Geological Survey Sweden Abisko ABK AE

Swedish Geological Survey Sweden Lovoe LOV K

British Geological Survey United Kingdom Eskdalemuir ESK K

British Geological Survey United Kingdom Hartland HAD K

British Geological Survey United Kingdom Lerwick LER K

US Geological Survey United States Barrow BRW AE

US Geological Survey United States College CMO AE

US Geological Survey United States Fredericksburg FRD K

US Geological Survey United States Honolulu HON D

US Geological Survey United States San Juan SJG D

US Geological Survey United States Sitka SIT K

Figure M31 Map showing geographic distribution of magnetic index observatories.

510 MAGNETIC INDICES

now the partial necklace of northern hemisphere observatories is used

to calculate an approximate AE.

The calculation of AE is relatively straightforward. One-min reso-

lution data from auroral observatories are used, and the average hori-

zontal intensity during the five magnetically quietest days is

subtracted. The total range of the data from among the various AE

observatories for each minute is measured, with AU being the highest

value and AL being the lowest value. The difference is defined as

AE ¼ AU  AL, and for completeness the average is also defined

as AO ¼ 1=2ðAU  ALÞ. For illustration, in Figure M34, we show

magnetograms from the eight auroral observatories contributing to

AE, during the Halloween Storm of 2003, along with the AE and its

attendant relatives.

Equatorial storm indices D

and A

sym

One of the most systematic effects seen in ground-based magnetometer

data is a general depression of the horizontal magnetic field as

recorded at near-equatorial observatories (Moos, 1910). This is often

interpreted as an enhancement of a westward magnetospheric equator-

ial ring current, whose magnetic field at the Earth’s surface partially

cancels the predominantly northerly component of the main field.

The storm-time disturbance index D

(Sugiura, 1964) is designed to

measure this phenomenon. D

is one of the most widely used indices

in academic research on the magnetosphere, in part because it is well

motivated by a specific physical theory.

The calculation of D

is generally similar to that of AE, but it is

more refined, since the magnetic signal of interest is quite a bit smaller.

One-min resolution horizontal intensity data from low-latitude obser-

vatories are used, and diurnal and secular variation baselines are sub-

tracted. A geometric adjustment is made to the resulting data from

each observatory so that they are all normalized to the magnetic equa-

tor. The average, then, is the D

index. It is worth noting that, unlike

the other indices summarized here, D

is not a range index. Its relative

sym

is a range index, however, determined by the difference between

the largest and smallest disturbance field among the four contributing

observatories.

In Figure M35 we show magnetograms from the four observatories

contributing to D

and A

sym

, for the Halloween storm of 2003, along

with the indices themselves. The commencement of the storm is easily

identified, and although the magnetic field is very disturbed during the

first hour or so of the storm, the disturbance shows pronounced long-

itudinal difference, and hence a dramatically enhanced A

sym

. With the

subsequent worldwide depression of H through to the beginning of

day 303 the storm is at its main phase of development. During this

time D

becomes increasingly negative. It is of interest to note that

it is during this main phase that AE is also rapidly variable, signally

the occurrence of substorms with the closure of magnetospheric elec-

tric currents through the ionosphere. AE diminishes during the recov-

ery period of the storm as D

also pulls back for its most negative

values and A

sym

is diminished. Toward the end of day 303 the second

act of this complicated storm begins, with a repeat of the observed

relationships of the various indices.

Figure M32 Example of (a) magnetometer data, horizontal

intensity (H) from the Fredericksburg observatory recording the

Halloween Storm of 2003, (b) the maximum range of H during

discrete 3 h intervals, and (c) the K index for Fredericksburg.

Figure M33 Example of (a) magnetometer data, horizontal

intensity (H), from the observatories used in the calculation of the

index, together with (b) the corresponding K

index. The

observatories have been grouped into North American, European,

and southern hemisphere regions in order to highlight similarities

of the data within each region and differences in the data across

the globe.

MAGNETIC INDICES 511

Ava ilability

Magnetic indices are routinely calculated by a number of different

agencies. Intermagnet agencies routinely calculate K indices for their

observatories (www.intermagnet.org). The GeoForschungsZentrum in

Potsdam calculates K

(www.gfz-potsdam.de). The Kyoto World Data

Center calculates AE and D

(swdcwww.kugi.kyoto-u.a c.jp). Other

agencies supporting the archiving and distribution of the indices

include the World Data Centers in Copenhagen (web.dmi.dk/fsweb/

projects/wdcc 1) and Boulder (www.ngdc.noaa.gov), as well as the

International Service of Geomagnetic Indices in Paris (www.cetp.

ipsl.fr).

Jeffrey J. Love and K.J. Remick

Bibliography

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Davis, T.N., and Sugiura, M., 1966. Auroral electrojet activity index

AE and its universal time variations. Journal of Geophysical

Research, 71: 785–801.

Mayaud, P.N., 1980. Derivation, Meaning, and Use of Geomagnetic

Indices, Geophysical Monograph 22. Washington, DC: American

Geophysical Union.

McPherron, R.L., 1995. Standard indices of geomagnetic activity. In

Kivelson, M.G., and Russell, C.T. (eds.), Introduction to Space Phy-

sics. Cambridge, UK: Cambridge University Press, pp. 451–458.

Menvielle, M., and Berthelier, A., 1991. The K-derived planetary

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(ed.), Geomagnetism , Vol. 2. London, UK: Academic Press,

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Sugiura, M., 1964. Hourly values of equatorial D

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2004SW000089.

Cross-references

IAGA, International Association of Geomagnetism and Aeronomy

Ionosphere

Magnetosphere of the Earth

MAGNETIC MINERALOGY, CHANGES

DUE TO HEATING

Mineralogical alterations occur very often in rocks subjected to ther-

mal treatment. Laboratory heating may cause, in many cases, not only

magnetic phase transformations, but also changes in the effective mag-

netic grain sizes, the internal stress, and the oxidation state. The pre-

sence or absence of such alterations is crucial to the validity and

success of numerous magnetic studies.

The basic assumption in paleointensity determinations in the mea-

surement of anisotropy of thermoremanent magnetization is that the

rock is not modified during the different successively applied heating

treatments. For simple thermal demagnetization, the occurrence of

mineralogical alteration can introduce errors in the determination of the

magnetic carrier if the latter had undergone transformation a at lower

Figure M34 Example of (a) magnetometer data, horizontal

intensity (H ), from the observatories used in the calculation of the

AE indices, together with (b) the corresponding AU and AL indices

and the (c) AE and AO indices.

Figure M35 Example of (a) magnetometer data, horizontal

intensity (H ), from the observatories used in the calculation of the

indices, together with (b) the corresponding D

plotted as the

center trace and the maximum and minimum disturbance values,

the difference of which is A

sym

512 MAGNETIC MINERALOGY, CHANGES DUE TO HEATING

temperature than its unblocking temperature. Acquisition of parasitic

chemical remanent magnetization is also possible if the heating was

not made in a perfectly zero magnetic field. Formation of magnetic

grains with very short relaxation times can lead to a large variation

in the magnetic viscosity, making the stable components of the rema-

nent magnetization sometimes immeasurable during thermal demagne-

tization. The interpretation of the results obtained by the Lowrie’s

method (1990) of identification of magnetic minerals by their coerciv-

ity and unblocking temperatures can be biased by mineralogical altera-

tion, because rock can undergo mineralogical alteration instead of

thermal demagnetization.

Analysis of the Curie curve (the measurement of the susceptibility in

the low- or high magnetic field as a function of the temperature) is a key

method for the identification of magnetic minerals, because each

mineral has its Curie temperature (corresponding to a change from a fer-

rimagnetic to a paramagnetic state). On a Curie curve with increasing

temperature, the Curie temperature is shown as a strong decrease in

the susceptibility, sometimes preceded by an increase in susceptibility

(a Hopkinson peak). However, mineralogical alteration can also

increase or decrease susceptibility so it is not possible to discriminate

the Curie temperature or the Hopkinson peak from mineralogical altera-

tion from the shape of a simple curve directly until the highest tempera-

ture is reached, except if the heating and cooling curves are identical.

Example of mineralogical transformations

due to heating

The increase of susceptibility during heating is mainly due to the forma-

tion of iron oxides. A decrease in susceptibility is often related to trans-

formation of these oxides, such as in the oxidation of magnetite to

hematite. Magnetite growth between 500 and 725



C (susceptibility

increase) and the hematization of the magnetite at a higher temperature

(susceptibility decrease) have been pointed out in a study of biotite gran-

ites (Trindade et al., 2001). Furthermore, magnetic oxides can be formed

from iron sulfides (pyrite, pyrrhotite, greigite, troilite), carbonates (side-

rite, ankerite), silicates, other iron oxides or hydroxides (e.g., Schwartz

and Vaughan, 1972; Dekkers, 1990a,b). During heating, hexagonal pyr-

rhotite (antiferromagnetic) can be transformed first, to monoclinic pyrrho-

tite (ferrimagnetic) by partial oxidation to magnetite (Bina et al., 1991).

Pyrrhotite oxidizes mostly to magnetite at higher temperatures. Siderite

oxidizes to magnetite or maghemite when exposed to air, even at room

temperature but the oxidation is faster during heating (Ellwood et al.,

1986; Hirt and Gehring, 1991). Maghemite converts to hematite in the

temperature range from 250 to 750



C, depending on the grain size, degree

of oxidation, and the presence of defects in the crystallographic lattice

(Verwey, 1935; Özdemir, 1990). In the range 250–370



C, goethite is

transformed generally to very fine grains of hematite (Gehring and Heller,

1989; Dekkers, 1990b). Lepidocrocite starts to transform into superpara-

magnetic (SP) maghemite at 175



C, with further conversion of this

maghemite into hematite at around 300



C (Gehring and Hofmeister,

1994). In an oxidative atmosphere, ferrihydrite transforms into hematite

(Weidler and Stanjek, 1998). But, ferrihydrite heated in the presence of

an organic reductant forms magnetite and/or maghemite, or magnetite-

maghemite intermediates (Campbell et al., 1997). Exsolved magnetite

has been found in plagioclases, pyroxene, and micas. With increasing

temperature phyllosilicates undergo different reactions (Murad and

Wagner, 1998). Thus, new phases developed at high temperatures depend

on the composition of the original clay minerals, the firing temperature,

and the atmosphere around the samples (Osipov, 1978).

During thermal treatment, ferrimagnetic minerals can also be affected

by changes in the magnetic grain size (alteration, grain growth, or grain

breaking due to fast heating and cooling). Therefore, grain size depen-

dence of magnetic susceptibility is weak for pseudosingle-domain (PSD)

and multidomain (MD) magnetite grains (Hartstra, 1982), but becomes

important if the grain size variation is a transformation into SP—Single-

Domain (SD) or a SD—PSD transformation. The susceptibility of the SD

grains is lower than for the other grain sizes (Stacey and Banerjee, 1974).

Homogenization of the distribution of crystal defects can also have

significant effects, leading to an increase in the susceptibility of large

grains and in the redistribution of the domain wall. Inversion by filling

up by new cations of the vacancy sites within the crystal lattice (Bina

and Henry, 1990) can give significant susceptibility variations. This

last mechanism and grain breaking could be at the origin of susceptibility

variation since the heating takes place at relatively low temperatures.

Methods of analysis

A change of color of the sample is an indication of mineralogical

alteration, but not all mineralogical transformations of magnetic miner-

als do lead to such color changes. Moreover, such change can be lim-

ited to a very fine surface layer and concern only to paramagnetic or

diamagnetic minerals. Different investigations are therefore necessary

to determine the magnetic mineralogy characteristics.

To investigate the mineralogical alteration of magnetic minerals due

to heating, as a first possibility the simple observation of a thin section

or conduct a microprobe analysis. In practice, such an approach is

often difficult since alteration can have affected a limited part of the

magnetic minerals, which can be moreover of a very small size. It is

therefore easy to miss the modified minerals. However, when it works,

this method yields precise indications about the affected minerals.

Transformation of a nonferrimagnetic mineral to another nonferri-

magnetic mineral does not introduce a significant variation in suscept-

ibility. Since the mineralogical change of the ferrimagnetic phase

mostly corresponds on the contrary to the susceptibility change, mea-

surement of susceptibility is generally a simple, fast, and efficient

method to point out the alteration of the ferrima gnetic part. The least

time consuming and common approach uses the monitoring of the var-

iations of bulk magnetic susceptibility measured at room temperature

and then after subsequent thermal steps, for example during thermal

demagnetization.

The different parts of Curie curve measured during heating and

cooling respectively, are similar if no alterations have occurred. The

nonreversibility of the curve, on the contrary, indicates mineralogical

changes. Hrouda et al. (2003) proposed to make several Curie curves

for the same sample, with increasing maximum temperature, until

obtaining a nonreversible curve. A faster approach is to apply cooling

as soon as a significant susceptibility change occurs during heating. If

the cooling curve is similar to the heating curve, the sample can be

then heated again until the next significant susceptibility variation,

etc. (Figure M36). Comparison of the heating and cooling curves can

yield key information about the affected and altered minerals. If a

Curie point occurs only on the heating curve, the corresponding

mineral not disappeared. On the other hand, if this Curie point appears

on the heating curve at a higher temperature than a transformation, it is

Figure M36 Thermomagnetic curve (low field normalized

susceptibility K/K

as a function of the temperature T in



C) of a

dolerite sample during heating (thick line) and cooling (thin

line). Partial loop “a” corresponds to an absence of mineralogical

alteration (reversible curve) contrary to the final part “b” of the loop

(irreversible curve).

MAGNETIC MINERALOGY, CHANGES DUE TO HEATING 513

often difficult or even impossible to determine if this Curie tempera-

ture was associated with the preexisting or the newly formed mineral.

A Curie temperature occuring only on the cooling curve is related to a

newly formed mineral.

Van Velzen and Zijderveld (1992) proposed a complementary method

for monitoring mineralogical alteration by using not only the suscept-

ibility but several remanent magnetization characteristics. This time-

consuming method allows a much more precise study of the effect of

heating. However, if several different alterations had occurred during

the same thermal treatment, they cannot be distinguished using these

approaches.

Hysteresis loop analysis is another classical method in rock magnet-

ism, giving, in particular, data on grain size and coercivities of the

magnetic minerals. The sample is first subjected to a strong magnetic

field to obtain the saturation of the magnetization. The total magnetiza-

tion is then measured during progressive decrease of the field followed

by the application of an increasing field in the opposite direction until

obtaining the saturation of the magnetization in this opposite direction

(“descending” curve d, Figure M37). The “ascending” curve a is then

obtained by measurement of the total magnetization during a decrease

of the field in the opposite direction followed by an increase in the

field in the direction of the initial field. To further investigate the

mineralogical alteration, hysteresis loops at room temperature are mea-

sured before and after heating ( Figure M37a). Difference hysteresis

loops (J

b–a

) are obtained by subtraction for a same field (H) value of

the measured magnetization value before (J

) and after (J

) heating

in curves d and a, respectively (Figure M37b). They are sometimes

relatively complicated curves, but using the separation method pro-

posed by Von Dobeneck (1996) in two curves (half-difference and

half-sum), the interpretation becomes much easier (Figure M37c). In

particular, it is possible to discriminate characteristics (coercivity, mag-

netic field for saturation) of disappearing and occurring magnetic com-

ponents, even during the same thermal treatment (Henry et al., 2005).

Applications

If heating at a temperature T applied in laboratory introduces a miner-

alogical change, previous heating at the same temperature T should

have given the same transformation. The studied rocks in their present

state were therefore not subjected to this temperature before being

sampled. The minimum temperature to develop mineralogical change,

therefore, corresponds to the maximum temperature possibly under-

gone by the rock in the past (Hrouda et al., 2003). This is therefore

the maximum paleotemperature indicator. However, that means ob-

viously, the maximum temperature since the rock has the present

mineralogical composition, i.e. sometimes relatively recently in case

of weathering and low-temperature oxidation.

Modification of the magnetic fabric as a result of heating has been

applied to different types of rocks (see Magnetic susceptibility, aniso-

tropy, effects of heating). The outcome was sometimes a simple

enhancement of the fabric, but significant changes of the fabric have

also been obtained. It is moreover possible to determine the anisotropy

of magnetic susceptibility of the ferrimagnetic minerals formed or that

have disappeared during successive heatings. To this aim, the tensor

resulting from the subtraction of the tensors measured before and after

heating is used (Henry et al. , 2003). When a same magnetic fabric is

obtained from several following thermal steps, it cannot be related to

the randomly oriented ferrimagnetic minerals. Instead, the newly

formed fabric must be related to characteristics of the preexisting rock.

By comparing this ferrimagnetic mineral fabric with the initial whole

rock fabric, it is possible to distinguish cases where heating simply

enhances of preexisting fabric from those where thermal treatment

induces a different fabric. Relative to the preheated fabric, this different

fabric may simply be an inverse fabric or one whose principal suscept-

ibility axes are oriented in a different direction, relative to petrostruc-

tural elements other than those defining the initial magnetic fabric.

Important applications concerning all the methods, assumes that no

transformation occurred during heating. It is fundamentally important to

verify this assumption when paleointensity or anisotropy of thermore-

manent magnetization studies are carried out. It is important to point

out that mineralogical alteration can also have important implications

for all the studies using heating, such as Lowrie’s (1990) method of

identification of magnetic minerals (using corercivity and unblocking

temperatures) or even simple thermal demagnetization.

Bernard Henry

Bibliography

Bina, M., Corpel, J., Daly, L., and Debeglia, N., 1991. Transformation

de la pyrrhotite en magnetite sous l’effet de la temperature: une

source potentielle d’anomalies magnétiques. Comptes Rendus de

I’Académie des Sciences, Paris. 313(II): 487–494.

Bina, M., and Henry, B., 1990. Magnetic properties, opaque mineral-

ogy and magnetic anisotropies of serpentinized peridotites from

ODP hole 670A near Mid-Atlantic ridge. Physics of the Earth

and Planetary Interiors, 65:88–103.

Figure M37 Example of hysteresis loops (ascending—a and

descending—d curves) measured at room temperature on dolerite

sample after heating at 400 and at 550



C (a) and corresponding

difference loop (b). From curves (c) obtained from half-sum and

half-difference of the curves b, transformation of a magnetic

component with low coercivity and saturation field to another

magnetic phase with higher coercivity and saturation field can be

inferred (Henry et al., 2004): Part of the curves pointing out

disappearance (in grey) of component with low coercivity (1)

and moderate saturation field (2), and occurrence (in black) of

component with higher coercivity (3) and high saturation

field (4). Field H in T, Magnetization in A m

–1

514 MAGNETIC MINERALOGY, CHANGES DUE TO HEATING

Campbell, A.S., Schwertmann, U., and Campbell, P.A., 1997. Forma-

tion of cubic phases on heating ferrihydrite. Clay Minerals, 32:

615–622.

Dekkers, M.J., 1990a. Magnetic monitoring of pyrrhotite alteration

during thermal demagnetisation. Geophysical Research Letters,

17: 779–782.

Dekkers, M.J., 1990b. Magnetic properties of natural goethite —III.

Magnetic behaviour and properties of minerals originating from

goethite dehydration during thermal demagnetisation. Geophysical

Journal International, 103: 233–250.

Ellwood, B.B., Balsam, W., Burkart, B., Long, G.J., and Buhl, M.L.,

1986. Anomalous magnetic properties in rocks containing the

mineral siderite: paleomagnetic implications. Journal of Geophysi-

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Gehring, A.U., Heller, F., and 1989. Timing of natural remanent mag-

netization in ferriferous limestones from the Swiss Jura Mountains.

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Gehring, A.U., and Hofmeister, A.M., 1994. The transformation of

lepidocrocite during heating: a magnetic and spectroscopic study.

Clays and Clay Minerals, 42(4): 409–415.

Hartstra, R.L., 1982, Grain size dependence of initial susceptibility and

saturation magnetization-related parameters of four natural magne-

tites in the PSD-MD range. Geophysical Journal of the Royal

Astronomical Society, 71: 477–495.

Henry, B., Jordanova, D., Jordanova, N., Souque, C., and Robion, P.,

2003. Anisotropy of magnetic susceptibility of heated rocks. Tecto-

nophysics, 366: 241–258.

Henry, B., Jordanova, D., Jordanova, N., and Le Goff, M., 2005.

Transformations of magnetic mineralogy in rocks revealed by

difference of hysteresis loops measured after stepwise heating:

Theory and cases study. Geophysical journal International, 162:

64–78.

Hirt, A.M., and Gehring, A.U., 1991. Thermal alteration of the mag-

netic mineralogy in ferruginous rocks. Journal of Geophysical

Research, 96: 9947–9953.

Hrouda, F., Müller, P., and Hanak, J., 2003. Repeated progressive heat-

ing in susceptibility vs. temperature investigation: a new palaeo-

temperature indicator? Physics and Chemistry of the Earth, 28:

653–657.

Lowrie, W., 1990. Identification of ferromagnetic minerals in a rock by

coercivity and unblocking temperature properties.

Geophysical

Research Letters, 17: 159–162.

Murad, E., and Wagner, U., 1998. Clays and clay minerals: The firing

process. Hyperfine Interactions, 117: 337–356.

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Nedra.

Özdemir, Ö., 1990. High temperature hysteresis and thermoremanence

of single-domain maghemite. Physics of the Earth and Planetary

Interiors, 65: 125–136.

Schwartz, E.J., and Vaughan, D.J., 1972. Magnetic phase relations of

pyrrhotite. Journal of Geomagnetism and Geoelectricity, 24:

441–458.

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Rock Magnetism. Amsterdam: Elsevier, 195 pp.

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ite. Geophysical Research Letters, 28: 2687–2690.

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Cross-references

Chemical Remanent Magnetization

Depth to Curie Temperature

Magnetic Remanence, Anisotropy

Magnetic Susceptibility

Magnetic Susceptibility, Anisotropy

Magnetic Susceptibility, Anisotropy, Effects of Heating

Paleointensity: Absolute Determination Using Single Plagioclase

Creptals

MAGNETIC PROPERTIES, LOW-TEMPERATURE

Introduction

Use of magnetic measurements at cryogenic temperatures for charac-

terizing magnetic mineralogy of rocks was initiated in the early 1960s,

when it was realized that several minerals capable to carry natural

remanent magnetization (NRM), e.g., magnetite and hematite, show dis-

tinctive magnetic phase transitions below room temperature. In the last

decade, low-temperature magnetometry of rocks and minerals has seen

a new boost due to increasing availability of commercial systems cap-

able to carry out magnetic measurements down to and below 4.2 K.

Low-temperature magnetometry has the potential to complement con-

ventional high-temperature methods of magnetic mineralogy while

offering an advantage of avoiding chemical alteration due to heating.

This is especially important in the case of sedimentary rocks, which alter

much more readily upon heating. However, additional complications

may arise because of a possible presence in a rock of mineral phases

showing ferrimagnetic or antiferromagnetic ordering below room tem-

perature. On the other hand, these minerals are often of a diagnostic

value by themselves, being the signature of various rock-forming pro-

cesses. In all, low-temperature magnetometry is a valuable new tool in

rock and environmental magnetism.

Several factors control low-temperature behavior of remanent mag-

netization and low-field susceptibility of minerals and rocks. Phase

transitions, which may occur below room temperature, have the most

profound effect. Also of importance is the temperature variation of

the intrinsic material properties such as magnetocrystalline anisotropy

and magnetostriction. Low-temperature magnetic properties of miner-

als are also affected by their stoichiometry and degree of crystallinity.

Last but not least, low-temperature variation of remanence and

magnetic susceptibility is generally grain-size dependent. In particular,

ultrafine (say, <20 nm) grains show the distinct behavior called super-

paramagnetism, which manifests itself in a nearly exponential decrease

of remanence with increasing temperature due to a progressive

unblocking of magnetization by thermal activation. On the other hand,

all the above factors have relatively little effect on saturation magneti-

zation, which is primarily determined by chemical composition of the

material.

Measurements that can be used to characterize low-temperature mag-

netic properties of minerals and rocks include the following. Thermal

demagnetization of a saturation isothermal remanent magnetization

(SIRM) given at a low temperature, typically 10 K, is a relatively rapid

experiment and the most frequently used. Low-temperature magnetic

phase transitions generally manifest themselves in SIRM vs temperature

curves and are most useful as diagnostic features. However, in some

cases signature of a magnetic-phase transition can be confused with that

of a ferrimagnetic to paramagnetic transition if the transition tempera-

tures are in the same range. An example is the 34-K phase transition

in mineral pyrrhotite, which is fairly close to Néel temperatures of

MAGNETIC PROPERTIES, LOW-TEMPERATURE 515